Results 1 to 10 of about 322 (150)
High Perturbations of a Fractional Kirchhoff Equation with Critical Nonlinearities
AxiomsThis paper concerns a fractional Kirchhoff equation with critical nonlinearities and a negative nonlocal term. In the case of high perturbations (large values of α, i.e., the parameter of a subcritical nonlinearity), existence results are obtained by the
Shengbin Yu +2 more
doaj +4 more sources
Nontrivial Solutions for Time Fractional Nonlinear Schrödinger-Kirchhoff Type Equations
Discrete Dynamics in Nature and Society, 2017 We study the existence of solutions for time fractional Schrödinger-Kirchhoff type equation involving left and right Liouville-Weyl fractional derivatives via variational methods.
N. Nyamoradi +4 more
doaj +10 more sources
On the singularly perturbation fractional Kirchhoff equations: Critical case
Advances in Nonlinear Analysis, 2022 This article deals with the following fractional Kirchhoff problem with critical exponent a+b∫RN∣(−Δ)s2u∣2dx(−Δ)su=(1+εK(x))u2s∗−1,inRN,\left(a+b\mathop{\int }\limits_{{{\mathbb{R}}}^{N}}| {\left(-\Delta )}^{\tfrac{s}{2}}u\hspace{-0.25em}{| }^{2}{\rm{d ...
Gu Guangze, Yang Zhipeng
doaj +3 more sources
Ground state solutions for fractional p-Kirchhoff equation
Electronic Journal of Differential Equations, 2022 We study the fractional p-Kirchhoff equation $$ \Big( a+b \int_{\mathbb{R}^N}{\int_{\mathbb{R}^N}} \frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}\, dx\, dy\Big) (-\Delta)_p^s u-\mu|u|^{p-2}u=|u|^{q-2}u, \quad x\in\mathbb{R}^N, $$ where \((-\Delta)_p^s\) is the fractional p-Laplacian operator, a and b are strictly positive real numbers, \(s \in (0,1)\), \(1 < p ...
Lixiong Wang, Haibo Chen, Liu Yang
doaj +3 more sources
Fractional Kirchhoff equation with a general critical nonlinearity
Applied Mathematics Letters, 2017 In this paper, we study the fractional Kirchhoff equation with critical nonlinearity \begin{align*} \left(a+b\int_{\mathbb R^N}|(-Δ)^{\frac{s}{2}}u|^2dx\right)(-Δ)^su+u=f(u)\ \ \mbox{in}\ \ \mathbb R^N, \end{align*} where $N>2s$ and $(-Δ)^s$ is the fractional Laplacian with ...
Hua Jin
exaly +3 more sources
Advances in Nonlinear Analysis, 2022 This article deals with the degenerate fractional Kirchhoff wave equation with structural damping or strong damping. The well-posedness and the existence of global attractor in the natural energy space by virtue of the Faedo-Galerkin method and energy ...
Yang Wenhua, Zhou Jun
doaj +2 more sources
On a viscoelastic Kirchhoff equation with fractional Laplacian
Discrete and Continuous Dynamical Systems - Series SzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Yang, Zhang, Li
exaly +2 more sources
Multiplicity and asymptotic behavior of solutions to a class of Kirchhoff-type equations involving the fractional p-Laplacian [PDF]
Journal of Inequalities and Applications, 2018 The present study is concerned with the following fractional p-Laplacian equation involving a critical Sobolev exponent of Kirchhoff type: [a+b(∫R2N|u(x)−u(y)|p|x−y|N+psdxdy)θ−1](−Δ)psu=|u|ps∗−2u+λf(x)|u|q−2uin RN, $$\biggl[a+b \biggl( \int_{\mathbb {R}^{
Liejun Shen
doaj +2 more sources
Nonhomogeneous fractional $p$-Kirchhoff problems involving a critical nonlinearity
Electronic Journal of Qualitative Theory of Differential Equations, 2019 This paper is concerned with the existence of solutions for a kind of nonhomogeneous critical $p$-Kirchhoff type problem driven by an integro-differential operator $\mathcal{L}^{p}_{K}$.
Jiabin Zuo +3 more
doaj +4 more sources
Multiplicity of solutions for fractional p ( z ) $p ( z ) $ -Kirchhoff-type equation
Journal of Inequalities and ApplicationsThis work deals with the existence and multiplicity of solutions for a class of variable-exponent equations involving the Kirchhoff term in variable-exponent Sobolev spaces according to some conditions, where we used the sub-supersolutions method ...
Tahar Bouali +2 more
doaj +3 more sources